You can not achieve this with the Ti-nspire cx. Only the CAS version will give the square root form. On the CAS there is an option in the settings called "EXACT" under calculation mode. The cx does not have this mode.

You do not. The TINspire with TI-84 keyboard works as a TI-84 Silver edition. Its OS is update when the TINspire OS is updated. The Ti 84 OS's you find on the TI website are not for the TINspire with TI84 keyboard.